Relative nonhomogeneous Koszul duality
Abstract
This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announced in Section 0.4 of arXiv:0708.3398. We prove the Poincare-Birkhoff-Witt theorem in this context and construct the triangulated equivalences of derived Koszul duality. The duality between the ring of differential operators and the de Rham DG-algebra, with the ring of functions as the base ring, is the thematic example. The moderate generality level makes the exposition in this book more accessible than the very heavily technical Chapter 11 of arXiv:0708.3398.
Cite
@article{arxiv.1911.07402,
title = {Relative nonhomogeneous Koszul duality},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:1911.07402},
year = {2022}
}
Comments
LaTeX 2e with mathtools.sty and tikz-cd; 220 pages, 7 commutative diagrams. v.7: Subsection 0.11 and new Section 9 inserted; v.8: Lemma 3.7 inserted, Subsections 10.8-10.10 added -- this is intended as a complete version; v.9: seven references added; v.10: small things corrected, references updated -- this is intended as the final arXiv version (the publisher's version is much more complete)